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Extrapolation Convolution for Data Prediction on a 2-D Grid: Bridging Spatial and Frequency Domains With Applications

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    This study introduces an extrapolation convolution (EC) framework to improve deep learning extrapolation for image restoration and compressed sensing. The EC framework enhances model prediction beyond training data, outperforming traditional methods in image outpainting and compressed sensing MRI.

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    Area of Science:

    • Machine Learning
    • Deep Learning
    • Image Processing
    • Medical Imaging

    Background:

    • Convolutional Neural Networks (CNNs) struggle with extrapolation tasks beyond training data.
    • Traditional CNNs rely on interpolation, limiting their ability to predict unseen data in image restoration and compressed sensing.
    • Existing methods face challenges in accurately reconstructing images and preserving fine details when deviating significantly from training conditions.

    Purpose of the Study:

    • To address the limitations of CNNs in extrapolation for image restoration and compressed sensing.
    • To propose and evaluate an extrapolation convolution (EC) framework for improved prediction beyond training constraints.
    • To enhance image reconstruction quality and detail preservation in image outpainting and compressed sensing MRI.

    Main Methods:

    • Developed an extrapolation convolution (EC) framework modeling missing data prediction as a linear extrapolation problem within deep learning architectures.
    • Applied EC in encoder-decoder (EnDec) networks for image outpainting, replacing conventional interpolation.
    • Integrated EC into Fourier-based compressed sensing MRI (CS-MRI) for predicting high-frequency signals from undersampled measurements.

    Main Results:

    • The proposed EC-DecNet and FDRN models demonstrated superior performance compared to traditional CNN-based models.
    • Achieved high-quality image reconstruction with finer details, evidenced by improved PSNR, SSIM, KID, and FID scores.
    • EC effectively reduced artifacts in image outpainting and preserved subtle structural details in CS-MRI at high acceleration factors.

    Conclusions:

    • The extrapolation convolution (EC) framework significantly enhances deep learning model performance in extrapolation tasks.
    • EC offers a robust solution for image restoration and compressed sensing, particularly in scenarios with limited training data or significant deviations.
    • Further research into larger kernel sizes and multilevel semi-supervised learning can further optimize extrapolation accuracy in frequency-domain applications like CS-MRI.